Let f: R → R be a function which satisfies f(x+y)=f(x)+f(y) ∀ x, y ∈ R. If f(1)=2 and g( n )=Σ_k =1^( n -1) f( k ), n ∈ N then the value of n, for…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a function which satisfies $\displaystyle f(x+y)=f(x)+f(y) \forall x, y \in \mathbf{R}$. If $\displaystyle f(1)=2$ and $\displaystyle g(\mathrm{n})=\sum_{\mathrm{k}=1}^{(\mathrm{n}-1)} f(\mathrm{k}), \mathrm{n} \in \mathbf{N}$ then the value of n, for which $\displaystyle g(\mathrm{n})=20$, is :